MATH 304 MIDDLE SCHOOL PROBLEM SOLVING #1


1. The sum of two different whole numbers is 12. What is the largest possible product that the two numbers can have?

2. How many natural numbers from 1 to 200 inclusive contain exactly one "1" ?

3. The edge of a cube is 9 ft. in length. A square has the same number of square units of area that the cube has in cubic units of volume. What is the length of a side of the square?

4. List all of the ways that the number 42 can be written as the SUM of two prime numbers.

5. A clock chimes once on each quarter hour, twice on the half hour, and the number of hours on the hour. How many times will the clock chime in a twenty-four hour period?

6. A palindromic number is one which reads the same forward and backwards. What is the next palindromic number after 67976?

7. If a full bottle weighs as much as three empty bottles, and two plates weigh as much as five empty bottles, how many full bottles will weigh the same as 16 empty bottles and 14 plates?

8. Carol and Jon collect eggs at the farm. One morning Carol said to Jon: "If you give me one egg, we will each have the same number of eggs." And Jon replied: "But if you give me one egg, I will have twice as many eggs as you." How many eggs did each of them collect that morning?

9. What is the smallest natural number greater than 1 which leaves a remainder of 1 when divided by 7 , 11 , and 13 ?

10. A worker received 2.5 times his regular hourly salary for working on a holiday. When he worked 2.5 hours on that holiday, he earned $21.25. What was his normal hourly wage?

11. When a seven is written at the right end of a 2-digit number, the value of the expression increases by 700. What was the original 2-digit number?

12. What is the LARGEST 8-digit number made up of the digits 1 , 1 , 2 , 2 , 3 , 3 , 4 and 4 so the ones are separated by one digit, the 2's by two digits, the 3's by three digits and the 4's by four digits?

13. A dollar was changed into 16 coins consisting of just nickels and dimes. How many of each were in the change?

14. When I multiply out 1 X 2 X 3 X ... X 98 X 99 X 100 , how many zeros are written at the end of the number which is the product?